Hi, we are from a bit further south in Springfield, and we have explored quite a few local areas. If you're interested in the Branson area, our favorite campground is Old 86, which is on the shores of Table Rock Lake. It doesn't have full hookups, but the sites are so amazing that it's worth it. I think they do have electric and water, with a dump station available. You can hop right in the lake from your campsite or go to their swim area.
We also really love Bennett Springs State Park, which is near Lebanon. If anyone in your family trout fishes, it's a great place to stay.
If you'd like to explore further south into Arkansas, Petit Jean is a really cool state park on a lake. There's a lot of neat hiking opportunities.
I'm not sure any of these places are really "resort-y," as we tend to prefer the state park style, but they are really pretty parks with natural amenities.
I've blogged about several of these places on my blog travelswithbirdy.com.